Method for Correcting A Synthetic Aperture Radar Antenna Beam Image

ABSTRACT

A method for correcting a synthetic aperture radar (SAR) antenna beam image comprising: collecting SAR data, forming an uncorrected image, isolating a pixel value from the uncorrected image, performing an inverse image formation on the isolated pixel value to convert the isolated pixel value into a phase history, calculating actual isolated pixel value location in the uncorrected image, computing range loss, antenna beam, and phase corrections for the isolated pixel value, interpolating range loss corrections, antenna beam pattern corrections, and phase corrections in the phase history, applying the interpolated corrections to the isolated pixel value phase history thereby forming a corrected phase history, converting the corrected phase history back into a corrected image, replacing the corresponding uncorrected pixel value in the uncorrected image with the corrected isolated pixel value, and repeating this process for all uncorrected pixel values thereby providing a corrected SAR image.

FIELD OF THE INVENTION

This invention relates generally to methods for correcting radar antennabeam patterns and, more particularly, to a method for correctingsynthetic aperture radar (SAR) antenna beam patterns.

BACKGROUND OF THE INVENTION

Synthetic Aperture Radar (SAR) is a type of radar that uses the relativemotion between a target and a sensor to produce high resolution imagesof that target. This relative motion can include a stationary target anda moving antenna or a moving target and a stationary antenna. A movingtarget and a stationary antenna are referred to as inverse syntheticaperture radar (ISAR). The distance the SAR device travels over a targetin the time taken for the radar pulses to return to the antenna createsa synthetic antenna aperture with finer resolution than the real beamaperture of the antenna. To create a SAR image, successive pulses ofradio waves are transmitted to “illuminate” a target scene, and the echoof each pulse is received and recorded. The pulses are transmitted andthe echoes received using a single beam-forming antenna, withwavelengths of a meter down to several millimeters. As a SAR device onboard a platform moves, the antenna location relative to the targetchanges with time. Signal processing of the successive recorded radarechoes allows the combining of the recordings from these multipleantenna positions. This process forms a synthetic antenna aperture andallows the creation of high-resolution images.

One of the challenges of increasing an imaging radar system'sinstantaneous radio frequency (RF) bandwidth is maintaining a constantantenna beam pattern. For a fixed physical aperture area of an antenna,by definition, the directivity, and pattern, varies as a function offrequency. The pattern changes are significant for close rangeinstrumentation radars that accurately measure the radar cross section(RCS) of objects from 2-18 GHz.

When collecting data in an ISAR collection mode, where the radar isstationary and the object is rotated as measurements are collected, thebeam pattern effects can be calibrated with a reference measurement of aknown object beforehand. This approach increases cost as the object tobe measured increases in size. In some cases, a large, specializedfacility is necessary to rotate the object. Forward operating areas withless infrastructure have need for a cost-effective instrumentation radarto scan an area of an aircraft, for example, to evaluate if maintenanceis needed for its radar reducing features. For this case the radar needsto move, not the object, to locate and measure RCS.

Existing beam pattern correction methods that approximate the beampattern as a polynomial cannot compensate for frequency variancesobserved and they assume the target response is present in allfrequencies and all measurement locations. Frequency dependent patterncorrections have been developed for range migration processing over a 2GHz bandwidth. Many radar systems use a uniform clutter field toestimate an antenna pattern but that requires both a uniform clutterfield and a constant gain over frequency, which may be difficult toobtain or maintain. At present, there is no satisfactory method orsystem that addresses the wide range of frequency or the wide range ofangles that occur with an instrumentation radar.

SUMMARY OF THE INVENTION

The present invention provides a method for correcting a syntheticaperture radar (SAR) image by collecting SAR data, including phasehistory and wave number domain, from an object, forming an uncorrectedimage I_(uc) of the object from the SAR collected data using aninvertible image formation algorithm, isolating a pixel value I_(uc)(x,y) from the uncorrected image I_(uc), then inserting that value intoanother image, I^(//) _(uc), the same size as I_(uc) with zero valuesfor all other pixels, performing an inverse image formation on the imageI^(//) _(uc), and converting the image into a phase history X^(//) _(v)that represents only the isolated pixel value I_(uc) (x,y). The relativelocation of the isolated pixel value I_(uc) (x,y) is calculated betweenevery radar measurement point to the actual isolated pixel's locationS_(x) ^(/)S_(y) ^(/).

Range loss corrections are computed for the isolated pixel value I_(uc)(x,y), based on the distance to the actual pixel value location S_(x)^(/)S_(y) ^(/). Antenna beam pattern corrections for the isolated pixelvalue I_(uc) (x,y) are computed based on frequency and angle to ameasurement location at every SAR sampling position. Phase correctionsfor the isolated pixel value I_(uc) (x,y) are calculated using an imageformation algorithm. Range loss corrections, antenna beam patterncorrections, and phase corrections are interpolated in a phase historydomain as X^(//) _(corr), according to the image formation algorithm.The interpolated phase history X^(//) _(corr) is applied to the phasehistory X^(//) _(v) forming a corrected phase history X^(///) _(v).

The corrected phase history X^(///) _(v) is converted back into an imageI^(//) _(c). The corresponding uncorrected pixel value I_(uc) (x,y) inthe uncorrected image I_(uc) is replaced with the corrected isolatedpixel value I^(//) _(c)(x,y). The above steps are repeated for eachuncorrected pixel value until all uncorrected pixel values in theuncorrected image I_(uc) are replaced with corrected pixels values fromI^(//) _(c), thereby providing a corrected SAR image of the object.

An advantage of the present invention is the ability to rapidly makecorrections to a radar image to bring a radar cross-section imagemeasurement closer to true radar cross-section.

Another advantage is the ability to use any invertible image formationalgorithm to form an uncorrected image and to use that image formationalgorithm to calculate corrections.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart of the steps of the method of the presentinvention.

FIG. 2 is a diagram of a rail SAR system.

FIG. 3A shows an un-corrected SAR antenna beam pattern image obtainedwith rail SAR computer simulation of 1.5-inch diameter metal spheres.

FIG. 3B shows the image of FIG. 3A after applying beam patterncorrection.

FIG. 4 illustrates an exemplary computing system that can be used inaccordance with the systems and methodologies disclosed.

DETAILED DESCRIPTION OF THE INVENTION

While the following description details the preferred embodiments of thepresent invention, it is to be understood that the invention is notlimited in its application to the details of arrangement of the parts asdescribed and shown in the figures disclosed herein, since the inventionis capable of other embodiments and of being practiced in various ways.

The present invention provides a method for implementing a frequency andspatially variant beam pattern correction for an instrumentation radarin a strip map SAR collection mode, wherein the correction relies solelyupon the measured antenna patterns and not upon any particular imagecontent to correct the image. The steps of the method are illustrated inthe flow chart of FIG. 1 . SAR image data is collected from an objectusing a synthetic aperture radar (SAR) (Step 1). The object can bestationary or moving. SAR data may be collected in a strip map SAR mode(Step 2) or into polar format (Step 3). If the SAR data is collectedinto a strip map SAR mode, the strip map SAR mode data may be convertedinto spotlight format data (Step 4). Methods for strip map datacollections are well known in the art. Strip map mode collects data in aconstant distance between pulses while the radar antenna is fixed at aparticular angle relative to the radar's motion.

Methods of spotlight data collection modes are well known in the art.Spotlight mode collects data at constant angle increments relative to adefined point in space and steers the antenna at that defined point inspace. Strip map data is converted to spotlight format by methods knownin the art where each collected pulse is shifted in time such that it isas if the radar flew a circle around a defined point. The defined pointin space is defined for ease to be the center of the final image and cancorrespond to the center of a collection rail SAR. The specific methodto make this correction depends upon the waveform used to collect SARdata.

For linear frequency modulated waveforms (only), the method includesdefining a value, R_line, of the distance between the center of theimage/target area and the position of the radar at the center of thecollection rail SAR. The method further includes defining a vector,R_point, of the distance between the center of the image/target area tothe location of the radar for each pulse collected. The rangedifference, defined as delR=R_line−R_point is then calculated and thefollowing correction is applied on a pulse-by-pulse basis as the rangedifference changes for each pulse:

${X_{v}^{\prime} = {X_{v}{\exp\left( {j\frac{2}{c}\left( {{2\pi f_{c}} + \gamma} \right)\Delta R} \right)}{\exp\left( {j\frac{2\gamma}{c^{2}}\Delta R^{2}} \right)}}},$

where X_(v) is the stripmap formatted phase history data and X_(v)′ isthe spotlight formatted phase history data.

An initial uncorrected image I_(uc) of the object is formed using apolar format algorithm (or another invertible image formation algorithm)(Step 5). A beam correction is applied using any invertible imageformation algorithm. The polar format algorithm is used as an example.Invertible means that the image and collected data (i.e. phase history)can be transformed back and forth between the image and data domains.The transformation between image and phase history is a forward orreverse transformation.

The forward transformation converts phase history to an image. Thereverse transformation converts the image to a phase history. Anexpression to describe the forward transformation from the phasehistory, X′_(v), to an uncorrected image, is I_(uc)=

{X′_(v)}.

Steps 6-14 are performed for each uncorrected pixel value I_(uc) (x,y)in the initial uncorrected image I_(uc). A new image, I^(//) _(uc), iscreated the same size as I_(uc) that contains all zero values except forthe isolated pixel from the uncorrected image I_(uc) an inverse imageformation is then performed, converting the isolated pixel value I^(//)_(uc), into a phase history X^(//) _(v). (Step 6). This step 6 can beimplemented in a loop for every image pixel in I_(uc). Otherimplementations include processing all image pixels at the same time, inparallel. The steps for each pixel in the uncorrected image are:selecting a pixel, zero valuing the remainder of the image pixels, andcreating a single pixel value image, I″_(uc), of the same size as theuncorrected image, I_(uc). Then reverse transform image I″_(uc), into aphase history, X″_(v), that represents only that pixel location:

X″ _(v)=

⁻¹ {I″ _(uc)}.

The actual location for each pixel is calculated in the uncorrectedimage based on detected pixel location (Step 7). The pixel location isrelative to a reference point. The reference point can be definedanywhere. It is convenient to define the center of the image as thereference point. The pixel location is calculated as the number ofpixels from the reference point, then multiplied by the pixel spacing.The pixel location relative to the reference point is now known.

In many image formation algorithms, and depending on how the data arecollected, the image pixel location (S_(x), S_(y)) is distorted from itstrue spatial location due to the radar's wavefront curvature (SeeDoerry, A W, “Wavefront curvature limitations and compensation to polarformat processing for synthetic aperture radar images.,” SAND2007-0046,902879, Jan. 2006. doi: 10.2172/902879, which is incorporated herein byreference). Step 7 estimates the actual spatial position (S_(x)′ S_(y)′)of that pixel location. Specifically, for the polar format algorithm ata close-range radar system, the true pixel location is a lineartransform that requires calculating Δr and α. The distance from theradar data collection locations to the reference point (in this case thecenter of the image) is R_(point),

$\alpha = {\tan^{- 1}\left( \frac{s_{x}}{R_{point}({midAperture})} \right)}$

where R_(point)(midAperture) is the closest distance, the radarapproaches the reference point (this calculation assumes that the imageis being formed at this location and orientation.):

${{\Delta r} = {\left( {{R_{point}({midAperture})} + s_{y}} \right)*\left( {\frac{1}{\cos(\alpha)} - 1} \right)}},$

the actual pixel location is then calculated (s′_(x),s′_(y)) as:

s′ _(y) =s _(y) −Δr

s′ _(x)=tan(α)*(R _(point)(midAperture)+s _(y)).

The range loss corrections are computed based on range to actual pixellocation (Step 8). Range loss is calculated using a radar rangeequation, based on the Friis transmission equation(https://en.wikipedia.org/wiki/Friis_transmission_equation). In theradar range equation, range loss is a term in the dominator, to thefourth power. The radar collects data based on the range to scenecenter. When the scene size is large relative to the distance to theradar, the R⁴ varies significantly over the entire scene. The assumedrange used thus far in processing needs to be removed before the actualrange to this pixel location is used to adjust the received power level.Fundamentally, targets that are closer in range return more power thanthe radar expects. This correction will adjust this difference.

The range loss correction is made on a pulse-by-pulse basis. For eachposition of the radar collected data, the distance to the referencepoint is calculated as Rng_(ref). Since the distance between the actualpixel location (s′_(x),s′_(y)) and each position the radar collecteddata is calculated as Rng_(target), the correction factor for range losscan be calculated as

${Rng}_{fac} = \sqrt{\frac{{Rng}_{ref}^{4}}{{Rng}_{target}^{4}}}$

Antenna beam pattern corrections are computed as a matrix based onfrequency and angle to a measurement location at every sample position(Step 9). Antenna beam pattern corrections are computed as a matrixbased on frequency and angle between target true location and all radarmeasurement locations. Some radars use the same antenna for bothtransmit and receive. One method to calculate this angle is to firstdefine a normal vector that represents the relative position to theradar measurement locations and pointing direction of the transmit andreceive antenna(s). The radar measurement positions are then used withthe relative antenna location to calculate an absolute location for eachtransmit and receive antenna at all radar measurement locations. Anothervector from the transmit and receive antenna to the actual pixellocation is calculated. The angle between these two vectors is thencalculated. A dot product is one way to compute the angle between thetwo vectors. The computed angle at each location is then used tointerpolate the antenna gain from a stored set of antenna patternmeasurement data; this antenna gain is G_(Tx) and G_(Rx).

Antenna pattern measurement data will have two dimensions to expressantenna gain: angle and frequency. Antenna pattern angle and frequencydata can be measured independently of the radar system to characterizethe antennas. The frequency points from the antenna pattern measurementdata can be interpolated to match the same frequency support points andspan as the phase history data.

An antenna gain factor correction, Amp_(fac), is calculated and appliedon a per-pulse basis. Each pulse has a unique angle from the antenna tothe true pixel location (calculated as described in the aboveparagraph). The collected data may or may not be calibrated to aspecific RCS value at a specific location. In the case the data has beencalibrated, the calibration needs to be removed before applying thisantenna correction. The antenna gain is calculated in the same way as itis calculated for the true pixel location, except the reference point isused instead of the true pixel location, which is G_(refTx) andG_(refRx).

${Amp}_{fac} = \frac{G_{Tx}G_{Rx}}{G_{refTx}G_{refRx}}$

Phase corrections are calculated based on a suitable image formationalgorithm known in the art (Step 10). For an example, see Doerry,“Wavefront Curvature Limitations and Compensation to Polar FormatProcessing for Synthetic Aperture Radar Images”, page 12, equations114-124. The phase corrections are expressed as Phase_(fac).

Range loss corrections, antenna beam pattern corrections, and phasecorrections are interpolated in the wave number domain according to theimage formation method (Step 11). The phase corrections are calculatedin the phase history domain based on the radar position as data iscollected. The processes used in the image formation process are appliedto convert the correction data to the same state as the reversetransformed image. Specifically, for use with a polar format algorithm,this process is a data resampling in the slow-time dimension. In thepresent implementation, correction data is created on resampled gridcoordinates in the fast-time dimension (of the phase history). This isaccomplished by resampling the antenna pattern data in the frequencydimension to correspond to the frequency points used in polar format toprovide an interpolated phase history X^(//) _(corr):

$X_{corr}^{''} = {{{resample}\left( \frac{{Phase}_{fac}}{{Rng}_{fac}{Amp}_{fac}} \right)}.}$

The interpolated corrections from Step 11 are applied to the phasehistory of the single pixel image I^(//) _(uc)(Step 12). This step 12 isa multiplication of each element of the phase history, X″_(v), with thesame corresponding frequency and angle element of the interpolated phasehistory, X″_(corr), of the single pixel:

X _(v) ′″=X _(v) ″o X _(corr)″.

The interpolated wavenumber domain data is converted back into an image(Step 13). This step 13 is a forward transformation, reversing Step 6.It creates a single pixel image with a corrected amplitude.

I _(c) ″

{X _(v)′″}

The pixel value is replaced in the uncorrected image with thecorresponding pixel value, I^(//) _(c)(x,y), in the image from Step 13.Then proceeding to the next pixel in the uncorrected image, steps 6-14are repeated until all pixels are corrected (Step 14).

In an alternate embodiment, corrections are made just to the antennabeam pattern, which is particularly useful for long range SAR systemswhere the range differences between near and far edges of the SAR imagedo not have a large variance in RCS due to relative change in distance.

A rail SAR system was computer simulated to generate SAR data from a setof objects to test the precision and accuracy of the method of thepresent invention. FIG. 2 provides a diagram of the simulated rail SARsystem 10. The SAR system 10 has a rail 11, an SAR 12, and SARtransmitting and receiving antennas 13. A scanned area 14 is shown as arectangle having a center location 15, a near location 16, and a farlocation 17. SAR data is collected during constant motion of the SAR 12across the rail 11 in a strip map SAR mode. The SAR 12 scans the area 14to measure the radar cross-section (RCS) of objects located within thatarea.

Rail SAR Computer Simulations

A test case of five 1.5-inch diameter metal spheres was created usingV-LOX electromagnetic software (IERUS Technologies, Inc., Huntsville,Ala., www.ierustech.com. V-Lox is a computational electromagneticsprediction software product based on method of moments and leveragesadvanced matrix compression and GPU acceleration to output high qualitysolutions quickly.) The sphere targets were positioned at a near corner16, near center, center 15, far center, and far corner 17 of a 5 ft-by-5ft area centered at a point 10 ft away from the radar (center location15 in FIG. 2 ). The simulation limited the frequency collection to 9-18GHz to make a more interpretable image. The same antenna pattern used tocreate the data was also used for correction.

FIG. 3A shows the un-corrected SAR image with range loss correctionsafter wavefront curvature correction and applying a Taylor window(nbar=4, SLL=−50 dB).). The target RCS values vary depending upon theirposition relative to the center of the image. The center target RCS isnearly correct, while targets at closer/farther ranges increasinglydeviate from true RCS. FIG. 3B shows the image after applying beampattern correction where the targets now vary within +/−0.5 dB of thetrue RCS. The true RCS of a 1.5-inch diameter sphere is −29.43 dBsm. Theaverage uncorrected RCS was −28.82 dBsm and the average corrected RCSwas −29.68 dBsm.

The computer simulations and SAR measurements show that the radarantenna beam pattern correction method of this invention improves theaccuracy of measured RCS values by bringing the measured RCS valuescloser to true RCS values.

FIG. 4 illustrates an exemplary computing system 30 that can be used inaccordance with the systems and methodologies disclosed. For example,the computing device 30 can be used to correct a synthetic apertureradar (SAR) antenna beam image as disclosed herein. The computing device30 includes at least one processor 31 that executes instructions thatare stored in a memory 32. The instructions may be, for instance,instructions for implementing functionality described as being carriedout by one or more components discussed above or instructions forimplementing one or more of the methods described above. The processor31 may access the memory 32 by way of a system bus 33. In addition tostoring executable instructions, the memory 32 may also store operatingparameters, required algorithm software, and so forth.

The computing device 30 additionally includes a data store 34 that isaccessible by the processor 31 by way of the system bus 33. The datastore 34 may include executable instructions, operating parameters, etc.The computing device 30 also includes an input interface 35 that allowsexternal devices to communicate with the computing device 30. Forinstance, the input interface 35 may be used to receive instructionsfrom an external computer device, from a user, etc. The computing device30 also includes an output interface 36 that interfaces the computingdevice 30 with one or more external devices. For example, the computingdevice 30 may display text, images, etc. by way of the output interface36.

Additionally, while illustrated as a single system, it is to beunderstood that the computing device 30 may be a distributed system.Thus, for example, several devices may be in communication by way of anetwork connection and may collectively perform tasks described as beingperformed by the computing device 30.

The foregoing description illustrates and describes the disclosure.Additionally, the disclosure shows and describes only the preferredembodiments but, it is to be understood that the preferred embodimentsare capable of being formed in various other combinations,modifications, and environments and are capable of changes ormodifications within the scope of the invention concepts as expressedherein, commensurate with the above teachings and/or the skill orknowledge of the relevant art. The embodiments described herein aboveare further intended to explain the best modes known by applicant and toenable others skilled in the art to utilize the disclosure in such, orother, embodiments and with the various modifications required by theparticular applications or uses thereof. Accordingly, the description isnot intended to limit the invention to the form disclosed herein. Also,it is intended that the appended claims be construed to includealternative embodiments. It will be further understood that variouschanges in the details, materials, and arrangements of the parts whichhave been described and illustrated above in order to explain the natureof this invention may be made by those skilled in the art withoutdeparting from the principle and scope of the invention as recited inthe following claims.

1. A computer and software implemented method for correcting a syntheticaperture radar (SAR) antenna beam image, comprising: a) collecting SARimage data, including phase history and wave number domain, from anobject; b) forming an uncorrected image I_(uc) of the object from theSAR collected data using an invertible image formation algorithm; c)isolating a pixel value I^(//) _(uc)(x,y) from the uncorrected imageI_(uc), then inserting the isolated pixel value I_(uc)(x,y) into animage with all pixel values having a zero value except the isolatedpixel value I_(uc) (x,y), thereby creating image I^(//) _(uc),performing an inverse image formation on the image I^(//) _(uc) tocreate a phase history X^(//) _(v), that represents only the isolatedpixel value I_(uc)(x,y) from the image I^(//) _(uc); d) detecting thelocation of the isolated pixel value I_(uc) (x,y) relative to areference point and calculating an actual isolated pixel value locationS_(x) ^(/)S_(y) ^(/), based on detected isolated pixel value location inthe uncorrected image I_(uc); e) computing range loss corrections forthe isolated pixel value I^(//) _(uc)(x,y), based on a range to actualpixel location; f) computing antenna beam pattern corrections for theisolated pixel value I^(//) _(uc) (x,y) based on frequency and angle toa measurement location at every SAR sampling position; g) calculatingphase corrections for the isolated pixel value I^(//) _(uc) (x,y) usingan image formation algorithm; h) interpolating range loss corrections,antenna beam pattern corrections, and phase corrections into aninterpolated phase history X^(//) _(corr) according to the imageformation algorithm of Step g); i) applying the interpolated phasehistory, X^(//) _(corr), to the phase history X^(//) _(v) forming acorrected phase history X^(///) _(v) representing I^(//) _(uc); j)reversing step c) by transforming the corrected phase history X^(///)_(v), into a corrected image I^(//) _(c); k) replacing the correspondinguncorrected pixel value I_(uc)(x,y) in the uncorrected image I_(uc) withthe corrected isolated pixel value I^(//) _(c)(x,y); and l) repeatingsteps c) through l) until all uncorrected pixel values in theuncorrected image I_(uc) are replaced with corrected pixel values fromimage I^(//) _(c), thereby providing a corrected SAR image of theobject.
 2. The computer and software implemented method of claim 1,further comprising, in step b), forming the uncorrected image I_(uc)using a forward transformation from the phase history of the SARcollected data.
 3. The computer and software implemented method of claim1, wherein, in step c), the step of converting the isolated pixel valueI″_(uc) (x,y) into a phase history X″_(v) comprises reverse transformingthe pixel image I″_(uc) into the phase history X″_(v).
 4. The computerand software implemented method of claim 1, further comprising, in stepd), calculating the pixel location of the isolated pixel value I^(//)_(uc) as the number of pixels the isolated pixel value I^(//) _(uc) isdistant from the reference point, multiplying the number of pixels bypixel spacing, and estimating the actual pixel location (s_(x)′ s_(y)′)of the isolated pixel value I^(//) _(uc).
 5. The computer and softwareimplemented method of claim 1, further comprising, in step e),calculating range loss using a radar range equation.
 6. The computer andsoftware implemented method of claim 1, further comprising, in step f),calculating an antenna beam factor correction Amp_(fac) for the isolatedpixel value I^(//) _(uc) (x,y) and applying the antenna beam factorcorrection to the isolated pixel value I^(//) _(uc) (x,y) on a per-pulsebasis.
 7. The computer and software implemented method of claim 1,further comprising, in step g), calculating phase corrections for theisolated pixel value I^(//) _(uc) (x,y) in the phase history X_(v)″based on the SAR position as the SAR collected data from the object. 8.The computer and software implemented method of claim 1, furthercomprising, in step i), correcting the amplitude of the corrected imageI^(//) _(c)″.
 9. A computer and software implemented method forcorrecting a synthetic aperture radar (SAR) antenna beam image,comprising: a) collecting SAR image data, including phase history andwave number domain, from an object; b) forming an uncorrected imageI_(uc) of the object from the SAR collected data using an invertibleimage formation algorithm, forming the uncorrected image using a forwardtransformation from the phase history of the SAR collected data; c)isolating a pixel value I^(//) _(uc) (x,y) from the uncorrected imageI_(n)c, then inserting the isolated pixel value I_(uc)(x,y) into animage with all pixel values having a zero value except the isolatedpixel value I_(uc)(x,y), thereby creating image I^(//) _(uc), performingan inverse image formation on the image I^(//) _(uc) to create a phasehistory X^(//) _(v), that represents only the isolated pixel valueI_(uc)(x,y) from the image I^(//) _(uc); d) detecting the location ofthe isolated pixel value I_(uc)(x,y) relative to a reference point andcalculating an actual isolated pixel value location S_(x) ^(/)S_(y)^(/), based on detected isolated pixel value location in the uncorrectedimage I_(uc), calculating the pixel location of the isolated pixel valueI^(//) _(uc) (x,y) as the number of pixels the isolated pixel valueI^(//) _(uc) (x,y) is distant from the reference point, multiplying thenumber of pixels by pixel spacing, and estimating the actual location(s_(x)′ s_(y)′) of the isolated pixel value I^(//) _(uc) (x,y); e)computing range loss corrections for the isolated pixel value I^(//)_(uc) (x,y), based on a range to actual pixel location; f) computingantenna beam pattern corrections for the isolated pixel value I^(//)_(uc) (x,y) based on frequency and angle to a measurement location atevery SAR sampling position; g) calculating phase corrections for theisolated pixel value I^(//) _(uc) (x,y) using an image formationalgorithm; h) interpolating range loss corrections, antenna beam patterncorrections, and phase corrections in the phase history X^(//) _(corr)according to the image formation algorithm of Step g); i) applying theinterpolated phase history X^(//) _(corr) to the phase history X^(//)_(v) forming a corrected phase history X^(///) _(v); j) reversing stepc) by transforming the corrected phase history X^(///) _(v) into acorrected image I^(//) _(c); k) replacing the corresponding uncorrectedpixel value I_(uc)(x,y) in the uncorrected image I_(uc) with thecorrected isolated pixel value I^(//) _(c)(x,y); and l) repeating stepsc) through l) until all uncorrected pixel values in the uncorrectedimage I_(uc) are replaced with corrected pixel values from image I^(//)_(c), thereby providing a corrected SAR image of the object.
 10. Thecomputer and software implemented method of claim 9, further comprising,in step e), calculating range loss using a radar range equation.
 11. Thecomputer and software implemented method of claim 9, further comprising,in step f), calculating an antenna beam pattern correction Amp_(fac) forthe isolated pixel value I^(//) _(uc) (x,y) and applying the antennabeam pattern correction to the isolated pixel value I^(//) _(uc) (x,y)on a per-pulse basis.
 12. The computer and software implemented methodof claim 9, further comprising, in step g), calculating phasecorrections for the isolated pixel value I^(//) _(uc) (x,y) in the phasehistory X_(v)″ based on the SAR position as the SAR collected data fromthe object.
 13. The computer and software implemented method of claim 9,further comprising, in step i), correcting the amplitude of thecorrected image I^(//) _(uc).
 14. A computer and software implementedmethod for correcting a synthetic aperture radar (SAR) antenna beamimage, comprising: a) collecting SAR image data, including phase historyand wave number domain, from an object; b) forming an uncorrected imageI_(uc) of the object from the SAR collected data using an invertibleimage formation algorithm, forming the uncorrected image using a forwardtransformation from the phase history of the SAR collected data; c)isolating a pixel value I^(//) _(uc) (x,y) from the uncorrected imageI_(uc), then inserting the isolated pixel value I_(uc)(x,y) into animage with all pixel values having a zero value except the isolatedpixel value I_(uc)(x,y), thereby creating image I^(//) _(uc), performingan inverse image formation on the image I^(//) _(uc) to create a phasehistory X^(//) _(v) that represents only the isolated pixel valueI_(uc)(x,y) from the image I^(//) _(uc); d) detecting the location ofthe isolated pixel value I^(//) _(uc) (x,y) relative to a referencepoint and calculating actual isolated pixel value location S_(x)^(/)S_(y) ^(/), based on detected isolated pixel value location in theuncorrected image I_(uc), calculating the pixel location of the isolatedpixel value I^(//) _(uc) (x,y) as the number of pixels the isolatedpixel value I^(//) _(uc) (x,y) is distant from the reference point,multiplying the number of pixels by pixel spacing, and estimating theactual location (s_(x)′ s_(y)′) of the isolated pixel value I^(//) _(uc)(x,y); e) computing range lost corrections for the isolated pixel valueI^(//) _(uc) (x,y), based on a range to actual pixel location, andcalculating range loss based on a radar range equation; f) computingantenna beam pattern corrections for the isolated pixel value I^(//)_(uc) (x,y) based on frequency and angle to a measurement location atevery SAR sampling position, calculating a range factor correctionAmp_(fac) for the isolated pixel, and applying the range factorcorrection to the isolated pixel on a per-pulse basis; g) calculatingphase corrections for the isolated pixel value I^(//) _(uc) (x,y) usingan image formation algorithm; h) interpolating range loss corrections,antenna beam pattern corrections, and phase corrections into aninterpolated phase history X^(//) _(corr) according to the imageformation algorithm of Step g) and calculating phase corrections for theisolated pixel value I^(//) _(uc) (x,y) in the phase history domainbased on the SAR position as the SAR collected data from the object; i)applying the interpolated phase history, X^(//) _(corr), to the phasehistory X^(//) _(v) forming an interpolated phase history X^(///) _(v)representing I^(//) _(uc) (x,y); j) reversing step c) by converting thecorrected phase history X^(///) _(v) into a corrected image I^(//) _(c);k) replacing the corresponding uncorrected pixel value I_(uc)(x,y) inthe uncorrected image I_(uc) with the corrected isolated pixel valueI^(//) _(c) (x,y); and l) repeating steps c) through l) until alluncorrected pixel values in the uncorrected image I_(uc) are replacedwith corrected pixel values from image I^(//) _(c), thereby providing acorrected SAR image of the object.
 15. The computer and softwareimplemented method of claim 14, further comprising, in step i),correcting the amplitude of the corrected image I^(//) _(c).
 16. Acomputer and software implemented method for correcting a syntheticaperture radar (SAR) antenna beam image, comprising: a) collecting SARimage data, including phase history and wave number domain, from anobject; b) forming an uncorrected image I_(uc) of the object from theSAR collected data using an invertible image formation algorithm; c)isolating a pixel value I^(//) _(uc) (x,y) from the uncorrected imageI_(uc), then inserting the isolated pixel value I_(uc)(x,y) into animage with all pixel values having a zero value except the isolatedpixel value I_(uc)(x,y), thereby creating image I^(//) _(uc), performingan inverse image formation on the image I^(//) _(uc) to create a phasehistory X^(//) _(v) that represents only the isolated pixel valueI_(uc)(x,y) from the image I^(//) _(uc); d) detecting the location ofthe isolated pixel value I_(uc)(x,y) relative to a reference point andcalculating an actual isolated pixel value location S_(x) ^(/)S_(y)^(/), based on detected isolated pixel value location in the uncorrectedimage I_(uc); e) computing antenna beam pattern corrections for theisolated pixel value I^(//) _(uc) (x,y) based on frequency and angle toa measurement location at every SAR sampling position; f) interpolatingantenna beam pattern corrections into an interpolated phase historyX^(//) _(corr) using an image formation algorithm; g) applying theinterpolated phase history, X^(//) _(corr), to the phase history X^(//)_(v) forming a corrected phase history X^(///) _(v) representing I^(//)_(uc); h) reversing step c) by transforming the corrected phase historyX^(///) _(v) into a corrected image I^(//) _(c); i) replacing thecorresponding uncorrected pixel value I_(uc)(x,y) in the uncorrectedimage I_(uc) with the corrected isolated pixel value I^(//) _(c)(x,y);and j) repeating steps c) through i) until all uncorrected pixel valuesin the uncorrected image I_(uc) are replaced with corrected pixel valuesfrom image I^(//) _(c), thereby providing a corrected SAR image of theobject.
 17. The computer and software implemented method of claim 16,further comprising, in step b), forming the uncorrected image I_(uc)using a forward transformation from the phase history of the SARcollected data.
 18. The computer and software implemented method ofclaim 17, wherein, in step c), the step of performing an inverse imageformation on the image I″_(uc) to create a phase history X″_(v)comprises reverse transforming the pixel image I″_(uc) into the phasehistory X″_(v).
 19. The computer and software implemented method ofclaim 18, further comprising, in step d), calculating the pixel locationof the isolated pixel value I^(//) _(uc) as the number of pixels theisolated pixel value I^(//) _(uc) is distant from the reference point,multiplying the number of pixels by pixel spacing, and estimating theactual pixel location (s_(x)′ s_(y)′) of the isolated pixel value I^(//)_(uc).
 20. The computer and software implemented method of claim 19,further comprising, in step g), correcting the amplitude of thecorrected image I^(//) _(c).